Question:
If Charles borrowed $3900 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
Correct Answer
$4134
Solution And Explanation
Solution
Given,
Principal (P) = $3900
Rate of Simple Interest (SI) = 3%
Time (t) = 2 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 3% simple interest means, Rate of Simple Interest (SI) is 3% per annum.
Method (1) Using Formula
Calculation of Simple Interest
Formula to Calculate Simple Interest
Simple Interest (SI) = Principal × Rate × Time
Thus, Simple Interest (SI) = $3900 × 3% × 2
= $3900 ×3/100 × 2
= 3900 × 3 × 2/100
= 11700 × 2/100
= 23400/100
= $234
Thus, Simple Interest = $234
Calculation of Amount
The total money paid to the lender by a borrower is called the Amount.
In other words, sum of priciple and interest is called the Amount.
Formula to Calculate the Amount
Amount = Principal + Interest
Thus, Amount = $3900 + $234
= $4134
Thus, Amount to be paid = $4134 Answer
Method (2)
Calculation of Amount when Principal, Rate of Simple Interest and Time are given
Calculation of Amount directly using Principal, SI, and Time
Formula to calculate the Amount
Amount (A) = Principal (P) + Principal(P) × Rate of Interest (SI) × Time (t)
⇒ A = P + PRT
Here in the question, P = $3900
Rate of Simple Interest (SI) or (R) = 3%
And, Time (t) = 2 years
Thus, Amount (A)
= $3900 + ($3900 × 3% × 2)
= $3900 + ($3900 ×3/100 × 2)
= $3900 + (3900 × 3 × 2/100)
= $3900 + (11700 × 2/100)
= $3900 + (23400/100)
= $3900 + $234 = $4134
Thus, Amount (A) to be paid = $4134 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 3%
This, means, $3 per $100 per year
∵ For $100, the simple interest for 1 year = $3
∴ For $1, the simple interest for 1 year = 3/100
∴ For $3900, the simple interest in 1 year
= 3/100 × 3900
= 3 × 3900/100
= 11700/100 = $117
Thus, simple interest for 1 year = $117
Therefore, simple interest for 2 years
= Simple interest for 1 year × 2
= $117 × 2 = $234
Thus, Simple Interest (SI) = $234
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3900 + $234
= $4134
Thus, Amount to be paid = $4134 Answer
Similar Questions
(1) If Robert paid $3348 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(2) Find the amount to be paid if Charles borrowed a sum of $5900 at 8% simple interest for 8 years.
(3) Mark took a loan of $6800 at the rate of 7% simple interest per annum. If he paid an amount of $11084 to clear the loan, then find the time period of the loan.
(4) Find the amount to be paid if Susan borrowed a sum of $5650 at 4% simple interest for 7 years.
(5) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 10% simple interest.
(6) If Margaret paid $5220 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(7) Calculate the amount due if Karen borrowed a sum of $3950 at 8% simple interest for 4 years.
(8) Donald took a loan of $7000 at the rate of 9% simple interest per annum. If he paid an amount of $12040 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 6% simple interest.
(10) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 3% simple interest?